Estimation of hop count in multi-hop wireless sensor networks with arbitrary node density

In multi-hop wireless sensor networks, the number of hops between the source and the destination has a significant impact on network performance and has been extensively identified in the literature. However, the methods most commonly used significantly underestimate the number of hops for sparse networks. The impact of node density is significant, and this factor is not adequately addressed. In effect, many schemes to calculate hop count imply geographic routing, even if they intend to consider the shortest path routes. Therefore, we propose a new technique for estimating hop count. We consider the hop progress when the network nodes are uniformly deployed and the shortest path between the source and the destination is selected. We determine a distribution of the remaining distance to destination. In order to correctly capture the situation for a sparse network, we examine the selection of the next neighbour node as a relaying node for the next hop. The analytical model is verified by simulation.